The single crystal of $Mg_{0.16}Zn_{0.84}$Te:Co(Co:0.01 mole%) was grown by vertical Bridgman method. The crystal structure of $Mg_{0.16}Zn$_{0.84}$Te:Co and optical absorption properties of this compound were studied. The grown single crystal has a cubic structure and a lattice constant a=6.1422 $AA$ were determined by X-ray diffraction. As a result of the optical absorption spectra of $Mg_{0.16}Zn_{0.84}$Te:Co, the intracenter transitions due to $Co^{2+}$ ions were detected for $A-band:^4A_2(^4F){ o}^4T_2(^4F),; B-band:^4A_2(^4F){ o}^4T_1(^4F), C- band:^4A_2(^4F){ o}^4T_1(^4P)$.The charge transfer transition near the absorption edge was observed in the wavelength range of 550 to 770 nm. According to the crystal field theory, the crystal field parameter(Dq) and the Racah parameter(B) were determined.